This paper describes a new method for the suppression of noise in images via the wavelet transform. The method relies on two measures. The first is a classic measure of smoothness of the image and is based on an approximation of the local Holder exponent via the wavelet coefficients. The second, novel measure takes into account geometrical constraints, which are generally valid for natural images. The smoothness measure and the constraints are combined in a Bayesian probabilistic formulation, and are implemented as a Markov random field (MRF) image model. The manipulation of the wavelet coefficients is consequently based on the obtained probabilities. A comparison of quantitative and qualitative results for test images demonstrates the improved noise suppression performance with respect to previous wavelet-based image denoising methods.

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We examine methods to assess the convergence of Markov chain Monte Carlo (MCMC) algorithms and to accelerate their execution via parallel computing. We propose a convergence measure based on the deviations between simultaneously running MCMC algorithms. We also examine the acceleration of MCMC algorithms when independent parallel samplers are used and report on some experiments with coupled samplers. As applications we use small Ising model simulations and a larger medical image processing algorithm.

A stochastical algorithm to improve the visual appearance of blood..vessel images is presented. Each pixel value in the output image represents the probability that the pixel belongs to a blood-vessel. The algorithm incorporates a Metropolis sampler that approximates a posterior distribution. We first describe this algorithm and present some results. in the second part, we focus on methods to assess the sampler convergence. For a first method some versions of the sampler algorithm are executed in parallel. We propose a convergence measure based on the deviations between the parallel versions. We compare this measure with one based on the analysis of the underlying Markov chains, by applying the measures to Ising model simulations. We also examine whether the parallel samplers can be used to accelerate the algorithm. 1 THE MRF..ALGOJUTHM We describe the algorithm for blood..vessel image improvement which was first proposed in.' It is called the MRF-algorithm since it is based on Markov Random Field (MRF) image models. Overview of the MRF-algorithmWe first generally specify the algorithm. The algorithm is aimed at improving three-dimensional Magnetic Resonance Angiography (MRA) images or two-dimensional Digital Subtraction Angiography (DSA) images before displaying them on two-dimensional media. Improvement of angiographic images means increasing the contrast between bloodvessel and nonb1ood-vessel pixels. Ideal MBA or DSA images would allow to distinguish bloodvessel from other tissue unambiguously. Whereas ideally a bright pixel represents blood-vessel tissue and a dark pixel any other tissue, there are pixels for which this is not true, called artifacts. To successfully remove artifacts the algorithm incorporates a model for the shape of blood vessels. In that way, bright pixels lying outside bloodvessels are eliminated as not conforming to the model, whereas dark pixels amidst probable blood-vessel pixels are restored as they fit the model well. The algorithm allows the user to specify the relative importance of shape and original gray-values (the latter is called the photometry). The result is not a binary decision as to whether a pixel belongs to a blood-vessel or not, but rather the probability that it belongs to a blood-vessel, according to how well it satisfies the models for the shape and the photometry. This leaves room for an expert decision.We now describe in more detail how the MRF-algorithm is worked out. Although as mentioned above no binary decisions are desired, let us consider two.. or three-dimensional binary images whose pixels each represent a small area or volume of the imaged tissue. Each of these binary pixels is assigned a label indicating whether or not the small area is a part of a blood-vessel. Such a binary image is thus an interpretation of the input image. While the true labeling is unknown, the input image contains imperfect information about it. The validity of this information is given by a statistical model. We additionally incorporate some constraints about the shape that is pre...

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